Chapter 3 Lecture 8. Drag polar 3. Topics. Chapter-3

Size: px
Start display at page:

Download "Chapter 3 Lecture 8. Drag polar 3. Topics. Chapter-3"

Transcription

1 Chapter 3 ecture 8 Drag polar 3 Topics Boundary layer separation, adverse pressure gradient and favourable pressure gradient Boundary layer transition Turbulent boundary layer over a flat plate General remarks on boundary layers Boundary layer separation, adverse pressure gradient and favourable pressure gradient When the flow takes place around airfoils and curved surfaces, the velocity outside the boundary layer is not constant. From Bernoulli s equation it can be deduced that when the velocity decreases the pressure increases and viceversa. When the velocity is decreasing i.e. dp/dx is positive, the pressure gradient is called Adverse pressure gradient. When dp/dx is negative it is called Favourable pressure gradient. Figure 3.4 shows the development of a boundary layer in an external stream with adverse pressure gradient (dp/dx > 0). Such a flow may occur on the upper surface of an airfoil beyond the point of maximum thickness. Since the static pressure at a station remains almost constant across the boundary layer, the pressure inside the boundary layer at stations separated by distance Δx also increases in the downstream direction. Dept. of Aerospace Engg., Indian Institute of Technology, Madras

2 Fig.3.4 Flow in boundary layer before and after point of separation (not to scale) Figure 3.4 also shows a small element ABCD in the boundary layer. The p+ dp/dx Δx. pressure on the face AD is p whereas that on the face BC is Since dp/dx is positive in this case, the net effect causes a deceleration of the flow, in addition to that due to viscosity. The effect is more pronounced near the surface and the velocity profile changes as shown in Fig.3.4. Finally at point S the slope of the velocity profile at the wall, U/ y wall, becomes zero. Besides the change in shape, the boundary layer also thickens rapidly in the presence of adverse pressure gradient. Downstream of the point S, there is a reversal of the flow direction in the region adjacent to the wall. A line can be drawn (indicated as dotted line in Fig.3.4) in such a way that the mass flow above this line is the same as that ahead of point S. Below the dotted line, there is a region of recirculating flow and the value of the stream function ψ for the dotted line is zero. However, ahead of the point S, the ψ =0 line is the surface of the body. Thus, after the point S, it is observed that between the main flow (i.e. region above ψ =0 line) and the body surface lies a region of recirculating flow. When this happens the flow is said to be Separated and S is referred to as the Point of separation. Due to separation, the pressure recovery, which would have taken Dept. of Aerospace Engg., Indian Institute of Technology, Madras 2

3 place in an unseparated flow, does not take place and the pressure drag of the body increases. Remarks: (i) If the adverse pressure gradient is very gradual then separation may not take place (Refer to Ch. 8 of Ref.3. for dp/dx needed for separation). (ii) Separation does not take place when the pressure gradient is favourable. (iii) In the two-dimensional case shown in Fig.3.4 the gradient U/ y is zero at the point of separation. Hence c f is zero at this point. This behaviour is used in computations to determine the location of the separation point Boundary layer transition In a laminar boundary layer, either the flow variables at a point have constant values or their values show a definite variation with time. However, as Reynolds number increases, it is found that the flow variables inside the boundary layer show chaotic variation with time. Such a boundary layer is called Turbulent boundary layer. The change over from laminar to turbulent boundary layer is called Transition and takes place over a distance called Transition length. Initiation of transition in a boundary layer, can be studied as an instability phenomenon. In this study, the flow is perturbed by giving a small disturbance and then examining whether the disturbance grows. Details of the analysis are available in chapter 5 of Ref.3. and chapter 5 of Ref.3.3. The salient features can be summarized as follows.. In a boundary layer on a flat plate with uniform external subsonic stream (U e = constant), the flow becomes sensitive to some disturbances as R x exceeds 5 x 0 5. This is called Critical Reynolds number (R crit ). For boundary layers in other cases, R crit depends on Mach number, surface curvature, pressure gradient in external stream and heat transfer from wall. Dept. of Aerospace Engg., Indian Institute of Technology, Madras 3

4 2. After R crit is exceeded, some disturbances grow. These are called Tollmien Schlichting (T-S) waves. 3. The T-S waves lead to three-dimensional unstable waves and formation of isolated large scale vortical structures called turbulent spots. 4. The turbulent spots grow and coalesce to form fully turbulent flow. Remarks: (i) As R crit is exceeded only some disturbances grow and hence in flows with very low free stream turbulence level, R crit as high as 2.8 x 0 6 has been observed in experiments. It may be recalled from fluid mechanics that the flow in pipe can become turbulent when Reynolds number, based on pipe diameter (R ed ), exceeds But laminar flow has been observed, in very smooth pipes, even at R ed = 40,000. (ii) Transition process takes place over a length called transition length. Reference 3., chapter 5 gives some guidelines for estimating this length. Surface roughness reduces this length. (iii) In flows with external pressure gradient, the transition is hastened by adverse pressure gradient. It is generally assumed that transition does not take place in favourable pressure gradient Turbulent boundary layer over a flat plate When the flow is turbulent, one of its dominant features is that the velocity at a point is a random function of time(fig.3.5). When a quantity varies in a random manner, one cannot say as to what the value would be at a chosen time, though the values may lie within certain limits. In such a situation, the flow features are described in terms of statistical averages. For example, the average Uof a fluctuating quantity U is given by : T 0 +T UT 0 = Udt 2T (3.3) T0 -T Dept. of Aerospace Engg., Indian Institute of Technology, Madras 4

5 Fig.3.5 Typical turbulence signal If the quantity U is independent of T 0 then the phenomenon is called Stationary random phenomenon. The discussion here is confined to this type of flow. In such a case, the instantaneous value, Ut =U+u t;u=u-u. Ut, is expressed as : By definition u = 0. Hence, to distinguish different turbulent flows the root mean square (r.m.s.) of the fluctuating quantity is used. u 2 rms = 2 u' = 2T T 2 u dt (3.32) -T T r.m.s. value of u is 2 u' Another feature of turbulent flows is that even if the mean flow is only in one direction, the fluctuations are in all three directions i.e. the instantaneous velocity vector ( V ) at a point would be V = U+u i+v j+w k;u,v andw are the components of the fluctuating velocity along x, y and z directions. Because of the random fluctuations, the transfer of heat, mass and momentum is many times faster in turbulent flows than in laminar flows. However, the part of Dept. of Aerospace Engg., Indian Institute of Technology, Madras 5

6 the kinetic energy of the mean motion which gets converted into the random fluctuations is finally dissipated into heat and as such losses are higher when the flow is turbulent. Characteristics of turbulent boundary layer: Analysis of turbulent boundary layer is more complicated than that of laminar boundary layer. Reference 3., chapters 6 to 22 can be referred to for details. A few results are presented below. Velocity profile: Velocity profile of a turbulent boundary layer on a flat plate with zero pressure gradient is also shown in Fig.3.2. The profile can be approximated by a power law like: U = y/δ U e /7 ;5 0 5 <Re<0 7 This approximation is called /7 th power law profile. Boundary layer thickness δ : Though the velocity gradient U/ y near the wall is much higher for (3.33) turbulent boundary layer than for the laminar case, the gradient is lower away from the wall and δ is much higher for a turbulent boundary layer. Reference 3.3, chapter 6, gives the following expression for δ. δ turb 0.6 = x R /7 x (3.34) Skin friction: The value of U/ y wall is higher for turbulent boundary layer than for laminar boundary layer (Fig.3.2). Hence, the skin friction drag for turbulent boundary layer is much higher than that for a laminar boundary layer. Reference 3.3, chapter 6 gives the following expression for C df C df = (3.35) R /7 Dept. of Aerospace Engg., Indian Institute of Technology, Madras 6

7 Remarks: (i) In Eqs.(3.34) and (3.35) it is assumed that the boundary layer is turbulent from the leading edge. Corrections to these expressions can be applied by taking the start of the transition region as the origin of the turbulent boundary layer. However, at the values of R obtained in actual airplanes the error in C df, by ignoring the laminar region is small. (ii) In certain references following expressions are found for δ and C df. 5 / 0.37/ x δ x = R and 5 C = / R. df However, Ref.3.3 chapter 6 shows that Eqs. (3.34) and (3.35) are more accurate. (iii) For the /7 th power law profile of the turbulent boundary layer (Eq.3.33), it can be shown using Eqs.(3.26) and (3.33) that : Example 3.2 δ δ = for turbulent boundary layer (3.36) Consider a case with = 0.5 m, V = 30m/s, =5 0 m /s which gives R = 0 6. Obtain the values of δ, δ and C df in the following cases. (i) Assume that the boundary layer is laminar throughout even at R = 0 6 (ii) Assume that the boundary layer is turbulent from landing edge of plate. Solution: (i) aminar flow δ 5 5 = = = R 0 or δ =2.5mm δ = = = R 0 or δ =0.86mm C df = = = R 0 (ii) Turbulent flow δ 0.6 = = R /7 or δ =.2mm Dept. of Aerospace Engg., Indian Institute of Technology, Madras 7

8 Remark : δ δ =.39mm C df = = = /7 R The comparison of the above results points out that the values of δ and δ are larger when the boundary layer is turbulent than when it is laminar. The value of C df in the former case is nearly three times of that in the later case General remarks on boundary layers In this subsection the following four topics are briefly touched upon. (i) Calculation of boundary layer, (ii) Separation of turbulent boundary layer, (iii) aminar flow airfoil and (iv) Effect of roughness on transition and skin friction (i) Calculation of boundary layer To calculate the boundary layer over an airfoil the first step is to obtain the velocity distribution using potential flow theory. It may be recalled from aerodynamics, that in potential flow analysis the velocity on the surface of the body is not zero. It is assumed that this velocity distribution, given by potential flow, would roughly be the distribution of velocity outside the boundary layer (U e ). From this velocity distribution and using Bernoulli s equation, the first estimate of dp/dx is obtained. Based on this data the growth of laminar boundary layer and the location of transition point are determined. After the transition, the growth of turbulent boundary layer is calculated. After obtaining the boundary layers the displacement thickness δ is added to the airfoil shape and calculations are repeated till the displacement thickness assumed at the beginning of an iteration is almost same as that obtained after calculation of the boundary layer. Subsequently, the skin friction drag can be calculated. Section 8.4 of Ref.3. may be consulted for details. Presently, Computational Fluid Dynamics (CFD) is used for these calculations. Dept. of Aerospace Engg., Indian Institute of Technology, Madras 8

9 (ii) Separation of turbulent boundary layer A turbulent boundary layer may also separate from the surface when it is subjected to adverse pressure gradient. However, due to turbulent mixing the value of U/ y w for separation to take place is much higher than that in the case of laminar boundary layer. Hence, a turbulent boundary layer has a higher resistance to separation. This behaviour is used in bluff bodies to delay the separation and reduce their pressure drag. For example, in the case of a circular cylinder the laminar boundary layer separates at around 80 0 leaving a large Fig.3.6 Schematic of flow past circular cylinder (a) aminar separation (b) Turbulent separation separated region (Fig.3.6a). However, if the transition to turbulent flow takes place before separation of laminar boundary layer, the separation is delayed. A o turbulent layer separates at around08, giving a smaller separated region (Fig.3.6b). Since the drag of a bluff body is mainly pressure drag, the total drag decreases significantly when the flow is turbulent before separation. For example, the drag coefficient of a circular cylinder is around when the separation is laminar and it is 0.3 when the separation is turbulent (Refer chapter of Ref.3.) (iii) aminar flow airfoils For a streamlined body, like an airfoil at low angle of attack, the drag is mainly skin friction drag. Figure 3.7 and Eqs.(3.30) and (3.35) indicate that C df is much higher when boundary layer is turbulent. Hence, to reduce the drag of the airfoil, Dept. of Aerospace Engg., Indian Institute of Technology, Madras 9

10 its shape is designed in such a way that the transition to turbulence is delayed and the flow remains laminar over a longer portion of the airfoil. These airfoils are called aminar flow or low drag airfoils. Presently, efforts are in progress to delay the transition by boundary layer control (see remark in section 3.7.2). Fig.3.7 Skin friction drag coefficient at various Reynolds numbers and levels of roughness (iv) Effect of roughness on transition It was mentioned that the critical Reynolds number (R crit ) depends on factors like pressure gradient, Mach number, surface curvature and heat transfer. However, the onset of transition may be delayed when disturbance like free stream turbulence is low. However, if the surface is rough, this delay may not be observed when roughness exceeds a certain value (see chapter 5 of Ref.3.) (v) Effect of roughness on skin friction in turbulent boundary layer Equation (3.35) indicates that C df is proportional to -/7 R i.e. C df decreases with R. However, when the surface is rough it is observed that the decrease in C df stops after a certain Reynolds number(fig.3.7). This Reynolds number is called Cut-off Reynolds number and is denoted by (Re) cut-off. Dept. of Aerospace Engg., Indian Institute of Technology, Madras 0

11 The roughness is quantified by the parameter ( l /k), where l = characteristic length e.g. the length () in case of a flat plate and chord (c) in case of an airfoil. k = height of roughness referred to as equivalent sand roughness. Following Ref.3.6, chapter 3, typical values of k are given in table 3.3. Type of surface Equivalent sand roughness (m) Natural sheet metal 4.06 x 0-6 Smooth paint 6.35 x 0-6 Standard camouflage paint.02 x 0-5 Mass production paint x 0-5 Table 3.3 Equivalent sand roughness for typical surfaces Based on Ref.3., chapter 8, Fig.3.7 shows typical plots of C df vs Re for turbulent boundary layer with l /k as parameter. For example, when l /k = 0 5, C df remains almost constant at beyond Re = 7 x 0 6. Reference 3.6 section 3. may be seen for plot of (Re) cutoff vs (l /k) with Mach number as parameter. These plots are based on section 4..5, of Ref.3.5. Dept. of Aerospace Engg., Indian Institute of Technology, Madras

M E 320 Professor John M. Cimbala Lecture 38

M E 320 Professor John M. Cimbala Lecture 38 M E 320 Professor John M. Cimbala Lecture 38 Today, we will: Discuss displacement thickness in a laminar boundary layer Discuss the turbulent boundary layer on a flat plate, and compare with laminar flow

More information

Chapter 5 Wing design - selection of wing parameters 2 Lecture 20 Topics

Chapter 5 Wing design - selection of wing parameters 2 Lecture 20 Topics Chapter 5 Wing design - selection of wing parameters Lecture 0 Topics 5..4 Effects of geometric parameters, Reynolds number and roughness on aerodynamic characteristics of airfoils 5..5 Choice of airfoil

More information

Fluid Mechanics. Chapter 9 Surface Resistance. Dr. Amer Khalil Ababneh

Fluid Mechanics. Chapter 9 Surface Resistance. Dr. Amer Khalil Ababneh Fluid Mechanics Chapter 9 Surface Resistance Dr. Amer Khalil Ababneh Wind tunnel used for testing flow over models. Introduction Resistances exerted by surfaces are a result of viscous stresses which create

More information

External Flow and Boundary Layer Concepts

External Flow and Boundary Layer Concepts 1 2 Lecture (8) on Fayoum University External Flow and Boundary Layer Concepts By Dr. Emad M. Saad Mechanical Engineering Dept. Faculty of Engineering Fayoum University Faculty of Engineering Mechanical

More information

Department of Mechanical Engineering

Department of Mechanical Engineering Department of Mechanical Engineering AMEE401 / AUTO400 Aerodynamics Instructor: Marios M. Fyrillas Email: eng.fm@fit.ac.cy HOMEWORK ASSIGNMENT #2 QUESTION 1 Clearly there are two mechanisms responsible

More information

UNIT IV BOUNDARY LAYER AND FLOW THROUGH PIPES Definition of boundary layer Thickness and classification Displacement and momentum thickness Development of laminar and turbulent flows in circular pipes

More information

1. Introduction, tensors, kinematics

1. Introduction, tensors, kinematics 1. Introduction, tensors, kinematics Content: Introduction to fluids, Cartesian tensors, vector algebra using tensor notation, operators in tensor form, Eulerian and Lagrangian description of scalar and

More information

Principles of Convection

Principles of Convection Principles of Convection Point Conduction & convection are similar both require the presence of a material medium. But convection requires the presence of fluid motion. Heat transfer through the: Solid

More information

Chapter 1 Lecture 2. Introduction 2. Topics. Chapter-1

Chapter 1 Lecture 2. Introduction 2. Topics. Chapter-1 Chapter 1 Lecture 2 Introduction 2 Topics 1.4 Equilibrium of airplane 1.5 Number of equations of motion for airplane in flight 1.5.1 Degrees of freedom 1.5.2 Degrees of freedom for a rigid airplane 1.6

More information

Lecture-4. Flow Past Immersed Bodies

Lecture-4. Flow Past Immersed Bodies Lecture-4 Flow Past Immersed Bodies Learning objectives After completing this lecture, you should be able to: Identify and discuss the features of external flow Explain the fundamental characteristics

More information

Day 24: Flow around objects

Day 24: Flow around objects Day 24: Flow around objects case 1) fluid flowing around a fixed object (e.g. bridge pier) case 2) object travelling within a fluid (cars, ships planes) two forces are exerted between the fluid and the

More information

DAY 19: Boundary Layer

DAY 19: Boundary Layer DAY 19: Boundary Layer flat plate : let us neglect the shape of the leading edge for now flat plate boundary layer: in blue we highlight the region of the flow where velocity is influenced by the presence

More information

WALL ROUGHNESS EFFECTS ON SHOCK BOUNDARY LAYER INTERACTION FLOWS

WALL ROUGHNESS EFFECTS ON SHOCK BOUNDARY LAYER INTERACTION FLOWS ISSN (Online) : 2319-8753 ISSN (Print) : 2347-6710 International Journal of Innovative Research in Science, Engineering and Technology An ISO 3297: 2007 Certified Organization, Volume 2, Special Issue

More information

and K becoming functions of Mach number i.e.: (3.49)

and K becoming functions of Mach number i.e.: (3.49) Chapter 3 Lecture 11 Drag polar 6 Topics 3.3.4 Parabolic drag polar at high speeds 3.3.5 Guidelines for variations of C Do and K for subsonic jet transport airplanes 3.3.6 Variations of C Do and K for

More information

Introduction to Turbulence AEEM Why study turbulent flows?

Introduction to Turbulence AEEM Why study turbulent flows? Introduction to Turbulence AEEM 7063-003 Dr. Peter J. Disimile UC-FEST Department of Aerospace Engineering Peter.disimile@uc.edu Intro to Turbulence: C1A Why 1 Most flows encountered in engineering and

More information

FLUID MECHANICS. Chapter 9 Flow over Immersed Bodies

FLUID MECHANICS. Chapter 9 Flow over Immersed Bodies FLUID MECHANICS Chapter 9 Flow over Immersed Bodies CHAP 9. FLOW OVER IMMERSED BODIES CONTENTS 9.1 General External Flow Characteristics 9.3 Drag 9.4 Lift 9.1 General External Flow Characteristics 9.1.1

More information

Applied Fluid Mechanics

Applied Fluid Mechanics Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 6. Flow of Fluid and

More information

Basic Fluid Mechanics

Basic Fluid Mechanics Basic Fluid Mechanics Chapter 6A: Internal Incompressible Viscous Flow 4/16/2018 C6A: Internal Incompressible Viscous Flow 1 6.1 Introduction For the present chapter we will limit our study to incompressible

More information

Given the water behaves as shown above, which direction will the cylinder rotate?

Given the water behaves as shown above, which direction will the cylinder rotate? water stream fixed but free to rotate Given the water behaves as shown above, which direction will the cylinder rotate? ) Clockwise 2) Counter-clockwise 3) Not enough information F y U 0 U F x V=0 V=0

More information

SPC Aerodynamics Course Assignment Due Date Monday 28 May 2018 at 11:30

SPC Aerodynamics Course Assignment Due Date Monday 28 May 2018 at 11:30 SPC 307 - Aerodynamics Course Assignment Due Date Monday 28 May 2018 at 11:30 1. The maximum velocity at which an aircraft can cruise occurs when the thrust available with the engines operating with the

More information

Wall treatments and wall functions

Wall treatments and wall functions Wall treatments and wall functions A wall treatment is the set of near-wall modelling assumptions for each turbulence model. Three types of wall treatment are provided in FLUENT, although all three might

More information

Physical Properties of Fluids

Physical Properties of Fluids Physical Properties of Fluids Viscosity: Resistance to relative motion between adjacent layers of fluid. Dynamic Viscosity:generally represented as µ. A flat plate moved slowly with a velocity V parallel

More information

5. Secondary Current and Spiral Flow

5. Secondary Current and Spiral Flow 5. Secondary Current and Spiral Flow The curve of constant velocity for rectangular and triangular cross-section obtained by Nikuradse are shown in Figures and 2. In all cases the velocities at the corners

More information

PART 1B EXPERIMENTAL ENGINEERING. SUBJECT: FLUID MECHANICS & HEAT TRANSFER LOCATION: HYDRAULICS LAB (Gnd Floor Inglis Bldg) BOUNDARY LAYERS AND DRAG

PART 1B EXPERIMENTAL ENGINEERING. SUBJECT: FLUID MECHANICS & HEAT TRANSFER LOCATION: HYDRAULICS LAB (Gnd Floor Inglis Bldg) BOUNDARY LAYERS AND DRAG 1 PART 1B EXPERIMENTAL ENGINEERING SUBJECT: FLUID MECHANICS & HEAT TRANSFER LOCATION: HYDRAULICS LAB (Gnd Floor Inglis Bldg) EXPERIMENT T3 (LONG) BOUNDARY LAYERS AND DRAG OBJECTIVES a) To measure the velocity

More information

Friction Factors and Drag Coefficients

Friction Factors and Drag Coefficients Levicky 1 Friction Factors and Drag Coefficients Several equations that we have seen have included terms to represent dissipation of energy due to the viscous nature of fluid flow. For example, in the

More information

Boundary-Layer Theory

Boundary-Layer Theory Hermann Schlichting Klaus Gersten Boundary-Layer Theory With contributions from Egon Krause and Herbert Oertel Jr. Translated by Katherine Mayes 8th Revised and Enlarged Edition With 287 Figures and 22

More information

Chapter 5 Phenomena of laminar-turbulent boundary layer transition (including free shear layers)

Chapter 5 Phenomena of laminar-turbulent boundary layer transition (including free shear layers) Chapter 5 Phenomena of laminar-turbulent boundary layer transition (including free shear layers) T-S Leu May. 3, 2018 Chapter 5: Phenomena of laminar-turbulent boundary layer transition (including free

More information

ROAD MAP... D-1: Aerodynamics of 3-D Wings D-2: Boundary Layer and Viscous Effects D-3: XFLR (Aerodynamics Analysis Tool)

ROAD MAP... D-1: Aerodynamics of 3-D Wings D-2: Boundary Layer and Viscous Effects D-3: XFLR (Aerodynamics Analysis Tool) AE301 Aerodynamics I UNIT D: Applied Aerodynamics ROAD MAP... D-1: Aerodynamics o 3-D Wings D-2: Boundary Layer and Viscous Eects D-3: XFLR (Aerodynamics Analysis Tool) AE301 Aerodynamics I : List o Subjects

More information

Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay

Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay Lecture No. # 35 Boundary Layer Theory and Applications Welcome back to the video course on fluid

More information

Visualization of flow pattern over or around immersed objects in open channel flow.

Visualization of flow pattern over or around immersed objects in open channel flow. EXPERIMENT SEVEN: FLOW VISUALIZATION AND ANALYSIS I OBJECTIVE OF THE EXPERIMENT: Visualization of flow pattern over or around immersed objects in open channel flow. II THEORY AND EQUATION: Open channel:

More information

9.4 Miscellaneous topics flight limitations, operating envelop and V-n diagram Flight limitations Operating envelop 9.4.

9.4 Miscellaneous topics flight limitations, operating envelop and V-n diagram Flight limitations Operating envelop 9.4. Chapter 9 Lecture 31 Performance analysis V Manoeuvres 4 Topics 9.4 Miscellaneous topics flight limitations, operating envelop and V-n diagram 9.4.1 Flight limitations 9.4.2 Operating envelop 9.4.3 V-n

More information

Fluid Mechanics Prof. T.I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture - 17 Laminar and Turbulent flows

Fluid Mechanics Prof. T.I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture - 17 Laminar and Turbulent flows Fluid Mechanics Prof. T.I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay Lecture - 17 Laminar and Turbulent flows Welcome back to the video course on fluid mechanics. In

More information

1. Fluid Dynamics Around Airfoils

1. Fluid Dynamics Around Airfoils 1. Fluid Dynamics Around Airfoils Two-dimensional flow around a streamlined shape Foces on an airfoil Distribution of pressue coefficient over an airfoil The variation of the lift coefficient with the

More information

BLUFF-BODY AERODYNAMICS

BLUFF-BODY AERODYNAMICS International Advanced School on WIND-EXCITED AND AEROELASTIC VIBRATIONS OF STRUCTURES Genoa, Italy, June 12-16, 2000 BLUFF-BODY AERODYNAMICS Lecture Notes by Guido Buresti Department of Aerospace Engineering

More information

S.E. (Mech.) (First Sem.) EXAMINATION, (Common to Mech/Sandwich) FLUID MECHANICS (2008 PATTERN) Time : Three Hours Maximum Marks : 100

S.E. (Mech.) (First Sem.) EXAMINATION, (Common to Mech/Sandwich) FLUID MECHANICS (2008 PATTERN) Time : Three Hours Maximum Marks : 100 Total No. of Questions 12] [Total No. of Printed Pages 8 Seat No. [4262]-113 S.E. (Mech.) (First Sem.) EXAMINATION, 2012 (Common to Mech/Sandwich) FLUID MECHANICS (2008 PATTERN) Time : Three Hours Maximum

More information

Masters in Mechanical Engineering. Problems of incompressible viscous flow. 2µ dx y(y h)+ U h y 0 < y < h,

Masters in Mechanical Engineering. Problems of incompressible viscous flow. 2µ dx y(y h)+ U h y 0 < y < h, Masters in Mechanical Engineering Problems of incompressible viscous flow 1. Consider the laminar Couette flow between two infinite flat plates (lower plate (y = 0) with no velocity and top plate (y =

More information

BOUNDARY LAYER FLOWS HINCHEY

BOUNDARY LAYER FLOWS HINCHEY BOUNDARY LAYER FLOWS HINCHEY BOUNDARY LAYER PHENOMENA When a body moves through a viscous fluid, the fluid at its surface moves with it. It does not slip over the surface. When a body moves at high speed,

More information

Part A: 1 pts each, 10 pts total, no partial credit.

Part A: 1 pts each, 10 pts total, no partial credit. Part A: 1 pts each, 10 pts total, no partial credit. 1) (Correct: 1 pt/ Wrong: -3 pts). The sum of static, dynamic, and hydrostatic pressures is constant when flow is steady, irrotational, incompressible,

More information

Turbulent Boundary Layers & Turbulence Models. Lecture 09

Turbulent Boundary Layers & Turbulence Models. Lecture 09 Turbulent Boundary Layers & Turbulence Models Lecture 09 The turbulent boundary layer In turbulent flow, the boundary layer is defined as the thin region on the surface of a body in which viscous effects

More information

ME19b. FINAL REVIEW SOLUTIONS. Mar. 11, 2010.

ME19b. FINAL REVIEW SOLUTIONS. Mar. 11, 2010. ME19b. FINAL REVIEW SOLTIONS. Mar. 11, 21. EXAMPLE PROBLEM 1 A laboratory wind tunnel has a square test section with side length L. Boundary-layer velocity profiles are measured at two cross-sections and

More information

Chapter 5 Performance analysis I Steady level flight (Lectures 17 to 20) Keywords: Steady level flight equations of motion, minimum power required,

Chapter 5 Performance analysis I Steady level flight (Lectures 17 to 20) Keywords: Steady level flight equations of motion, minimum power required, Chapter 5 Performance analysis I Steady level flight (Lectures 17 to 20) Keywords: Steady level flight equations of motion, minimum power required, minimum thrust required, minimum speed, maximum speed;

More information

6. Laminar and turbulent boundary layers

6. Laminar and turbulent boundary layers 6. Laminar and turbulent boundary layers John Richard Thome 8 avril 2008 John Richard Thome (LTCM - SGM - EPFL) Heat transfer - Convection 8 avril 2008 1 / 34 6.1 Some introductory ideas Figure 6.1 A boundary

More information

Chapter 5 Lecture 19. Performance analysis I Steady level flight 3. Topics. Chapter-5

Chapter 5 Lecture 19. Performance analysis I Steady level flight 3. Topics. Chapter-5 Chapter 5 Lecture 19 Performance analysis I Steady level flight 3 Topics 5.8 Influence of level flight analysis on airplane design 5.9 Steady level flight performance with a given engine 5.10 Steady level

More information

The Reynolds experiment

The Reynolds experiment Chapter 13 The Reynolds experiment 13.1 Laminar and turbulent flows Let us consider a horizontal pipe of circular section of infinite extension subject to a constant pressure gradient (see section [10.4]).

More information

ENGR Heat Transfer II

ENGR Heat Transfer II ENGR 7901 - Heat Transfer II External Flows 1 Introduction In this chapter we will consider several fundamental flows, namely: the flat plate, the cylinder, the sphere, several other body shapes, and banks

More information

Numerical Investigation of Thermal Performance in Cross Flow Around Square Array of Circular Cylinders

Numerical Investigation of Thermal Performance in Cross Flow Around Square Array of Circular Cylinders Numerical Investigation of Thermal Performance in Cross Flow Around Square Array of Circular Cylinders A. Jugal M. Panchal, B. A M Lakdawala 2 A. M. Tech student, Mechanical Engineering Department, Institute

More information

Fluid: Air and water are fluids that exert forces on the human body.

Fluid: Air and water are fluids that exert forces on the human body. Fluid: Air and water are fluids that exert forces on the human body. term fluid is often used interchangeably with the term liquid, from a mechanical perspective, Fluid: substance that flows when subjected

More information

Simulating Drag Crisis for a Sphere Using Skin Friction Boundary Conditions

Simulating Drag Crisis for a Sphere Using Skin Friction Boundary Conditions Simulating Drag Crisis for a Sphere Using Skin Friction Boundary Conditions Johan Hoffman May 14, 2006 Abstract In this paper we use a General Galerkin (G2) method to simulate drag crisis for a sphere,

More information

APPENDIX C DRAG POLAR, STABILITY DERIVATIVES AND CHARACTERISTIC ROOTS OF A JET AIRPLANE (Lectures 37 to 40)

APPENDIX C DRAG POLAR, STABILITY DERIVATIVES AND CHARACTERISTIC ROOTS OF A JET AIRPLANE (Lectures 37 to 40) APPENDIX C DRAG POLAR, STABILITY DERIVATIVES AND CHARACTERISTIC ROOTS OF A JET AIRPLANE (Lectures 37 to 40 E.G. TULAPURKARA YASHKUMAR A. VENKATTRAMAN REPORT NO: AE TR 2007-3 APRIL 2007 (REVISED NOVEMBER

More information

Outlines. simple relations of fluid dynamics Boundary layer analysis. Important for basic understanding of convection heat transfer

Outlines. simple relations of fluid dynamics Boundary layer analysis. Important for basic understanding of convection heat transfer Forced Convection Outlines To examine the methods of calculating convection heat transfer (particularly, the ways of predicting the value of convection heat transfer coefficient, h) Convection heat transfer

More information

(Refer Slide Time: 2:14)

(Refer Slide Time: 2:14) Fluid Dynamics And Turbo Machines. Professor Dr Shamit Bakshi. Department Of Mechanical Engineering. Indian Institute Of Technology Madras. Part A. Module-1. Lecture-3. Introduction To Fluid Flow. (Refer

More information

Steady waves in compressible flow

Steady waves in compressible flow Chapter Steady waves in compressible flow. Oblique shock waves Figure. shows an oblique shock wave produced when a supersonic flow is deflected by an angle. Figure.: Flow geometry near a plane oblique

More information

Introduction and Basic Concepts

Introduction and Basic Concepts Topic 1 Introduction and Basic Concepts 1 Flow Past a Circular Cylinder Re = 10,000 and Mach approximately zero Mach = 0.45 Mach = 0.64 Pictures are from An Album of Fluid Motion by Van Dyke Flow Past

More information

Lecture 7 Boundary Layer

Lecture 7 Boundary Layer SPC 307 Introduction to Aerodynamics Lecture 7 Boundary Layer April 9, 2017 Sep. 18, 2016 1 Character of the steady, viscous flow past a flat plate parallel to the upstream velocity Inertia force = ma

More information

Laminar Flow. Chapter ZERO PRESSURE GRADIENT

Laminar Flow. Chapter ZERO PRESSURE GRADIENT Chapter 2 Laminar Flow 2.1 ZERO PRESSRE GRADIENT Problem 2.1.1 Consider a uniform flow of velocity over a flat plate of length L of a fluid of kinematic viscosity ν. Assume that the fluid is incompressible

More information

5.8 Laminar Boundary Layers

5.8 Laminar Boundary Layers 2.2 Marine Hydrodynamics, Fall 218 ecture 19 Copyright c 218 MIT - Department of Mechanical Engineering, All rights reserved. 2.2 - Marine Hydrodynamics ecture 19 5.8 aminar Boundary ayers δ y U potential

More information

CLASS SCHEDULE 2013 FALL

CLASS SCHEDULE 2013 FALL CLASS SCHEDULE 2013 FALL Class # or Lab # 1 Date Aug 26 2 28 Important Concepts (Section # in Text Reading, Lecture note) Examples/Lab Activities Definition fluid; continuum hypothesis; fluid properties

More information

Introduction to Aerodynamics. Dr. Guven Aerospace Engineer (P.hD)

Introduction to Aerodynamics. Dr. Guven Aerospace Engineer (P.hD) Introduction to Aerodynamics Dr. Guven Aerospace Engineer (P.hD) Aerodynamic Forces All aerodynamic forces are generated wither through pressure distribution or a shear stress distribution on a body. The

More information

Chapter 10. Solids and Fluids

Chapter 10. Solids and Fluids Chapter 10 Solids and Fluids Surface Tension Net force on molecule A is zero Pulled equally in all directions Net force on B is not zero No molecules above to act on it Pulled toward the center of the

More information

Detailed Outline, M E 320 Fluid Flow, Spring Semester 2015

Detailed Outline, M E 320 Fluid Flow, Spring Semester 2015 Detailed Outline, M E 320 Fluid Flow, Spring Semester 2015 I. Introduction (Chapters 1 and 2) A. What is Fluid Mechanics? 1. What is a fluid? 2. What is mechanics? B. Classification of Fluid Flows 1. Viscous

More information

Vortex Induced Vibrations

Vortex Induced Vibrations Vortex Induced Vibrations By: Abhiroop Jayanthi Indian Institute of Technology, Delhi Some Questions! What is VIV? What are the details of a steady approach flow past a stationary cylinder? How and why

More information

Syllabus for AE3610, Aerodynamics I

Syllabus for AE3610, Aerodynamics I Syllabus for AE3610, Aerodynamics I Current Catalog Data: AE 3610 Aerodynamics I Credit: 4 hours A study of incompressible aerodynamics of flight vehicles with emphasis on combined application of theory

More information

Given a stream function for a cylinder in a uniform flow with circulation: a) Sketch the flow pattern in terms of streamlines.

Given a stream function for a cylinder in a uniform flow with circulation: a) Sketch the flow pattern in terms of streamlines. Question Given a stream function for a cylinder in a uniform flow with circulation: R Γ r ψ = U r sinθ + ln r π R a) Sketch the flow pattern in terms of streamlines. b) Derive an expression for the angular

More information

Chapter 9 Flow over Immersed Bodies

Chapter 9 Flow over Immersed Bodies 57:00 Mechanics of Fluids and Transport Processes Chapter 9 Professor Fred Stern Fall 009 1 Chapter 9 Flow over Immersed Bodies Fluid flows are broadly categorized: 1. Internal flows such as ducts/pipes,

More information

Fluid Mechanics II 3 credit hour. External flows. Course teacher Dr. M. Mahbubur Razzaque Professor Department of Mechanical Engineering BUET 1

Fluid Mechanics II 3 credit hour. External flows. Course teacher Dr. M. Mahbubur Razzaque Professor Department of Mechanical Engineering BUET 1 COURSE NUMBER: ME 323 Fluid Mechanics II 3 credit hour External flows Course teacher Dr. M. Mahbubur Razzaque Professor Department of Mechanical Engineering BUET 1 External flows The study of external

More information

Chapter 9 Flow over Immersed Bodies

Chapter 9 Flow over Immersed Bodies 57:00 Mechanics of Fluids and Transport Processes Chapter 9 Professor Fred Stern Fall 014 1 Chapter 9 Flow over Immersed Bodies Fluid flows are broadly categorized: 1. Internal flows such as ducts/pipes,

More information

Chapter 6 An introduction of turbulent boundary layer

Chapter 6 An introduction of turbulent boundary layer Chapter 6 An introduction of turbulent boundary layer T-S Leu May. 23, 2018 Chapter 6: An introduction of turbulent boundary layer Reading assignments: 1. White, F. M., Viscous fluid flow. McGraw-Hill,

More information

Numerical study of the effects of trailing-edge bluntness on highly turbulent hydro-foil flows

Numerical study of the effects of trailing-edge bluntness on highly turbulent hydro-foil flows Numerical study of the effects of trailing-edge bluntness on highly turbulent hydro-foil flows T. Do L. Chen J. Tu B. Anderson 7 November 2005 Abstract Flow-induced noise from fully submerged lifting bodies

More information

Part 3. Stability and Transition

Part 3. Stability and Transition Part 3 Stability and Transition 281 Overview T. Cebeci 1 Recent interest in the reduction of drag of underwater vehicles and aircraft components has rekindled research in the area of stability and transition.

More information

ENGINEERING FLUID MECHANICS. CHAPTER 1 Properties of Fluids

ENGINEERING FLUID MECHANICS. CHAPTER 1 Properties of Fluids CHAPTER 1 Properties of Fluids ENGINEERING FLUID MECHANICS 1.1 Introduction 1.2 Development of Fluid Mechanics 1.3 Units of Measurement (SI units) 1.4 Mass, Density, Specific Weight, Specific Volume, Specific

More information

External Flows. Dye streak. turbulent. laminar transition

External Flows. Dye streak. turbulent. laminar transition Eternal Flos An internal flo is surrounded by solid boundaries that can restrict the development of its boundary layer, for eample, a pipe flo. An eternal flo, on the other hand, are flos over bodies immersed

More information

UNIT II Real fluids. FMM / KRG / MECH / NPRCET Page 78. Laminar and turbulent flow

UNIT II Real fluids. FMM / KRG / MECH / NPRCET Page 78. Laminar and turbulent flow UNIT II Real fluids The flow of real fluids exhibits viscous effect that is they tend to "stick" to solid surfaces and have stresses within their body. You might remember from earlier in the course Newtons

More information

Chapter 2 Earth s atmosphere (Lectures 4 and 5)

Chapter 2 Earth s atmosphere (Lectures 4 and 5) Chapter 2 Earth s atmosphere (Lectures 4 and 5) Keywords: Earth s atmosphere; International standard atmosphere; geopotential altitude; stability of atmosphere. Topics 2.1 Introduction 2.2 Earth s atmosphere

More information

UNIT II CONVECTION HEAT TRANSFER

UNIT II CONVECTION HEAT TRANSFER UNIT II CONVECTION HEAT TRANSFER Convection is the mode of heat transfer between a surface and a fluid moving over it. The energy transfer in convection is predominately due to the bulk motion of the fluid

More information

Experimental and Numerical Investigation of Flow over a Cylinder at Reynolds Number 10 5

Experimental and Numerical Investigation of Flow over a Cylinder at Reynolds Number 10 5 Journal of Modern Science and Technology Vol. 1. No. 1. May 2013 Issue. Pp.52-60 Experimental and Numerical Investigation of Flow over a Cylinder at Reynolds Number 10 5 Toukir Islam and S.M. Rakibul Hassan

More information

J. Szantyr Lecture No. 4 Principles of the Turbulent Flow Theory The phenomenon of two markedly different types of flow, namely laminar and

J. Szantyr Lecture No. 4 Principles of the Turbulent Flow Theory The phenomenon of two markedly different types of flow, namely laminar and J. Szantyr Lecture No. 4 Principles of the Turbulent Flow Theory The phenomenon of two markedly different types of flow, namely laminar and turbulent, was discovered by Osborne Reynolds (184 191) in 1883

More information

Convection. forced convection when the flow is caused by external means, such as by a fan, a pump, or atmospheric winds.

Convection. forced convection when the flow is caused by external means, such as by a fan, a pump, or atmospheric winds. Convection The convection heat transfer mode is comprised of two mechanisms. In addition to energy transfer due to random molecular motion (diffusion), energy is also transferred by the bulk, or macroscopic,

More information

Physics 207 Lecture 18

Physics 207 Lecture 18 Physics 07, Lecture 8, Nov. 6 MidTerm Mean 58.4 (64.6) Median 58 St. Dev. 6 (9) High 94 Low 9 Nominal curve: (conservative) 80-00 A 6-79 B or A/B 34-6 C or B/C 9-33 marginal 9-8 D Physics 07: Lecture 8,

More information

Turbulence - Theory and Modelling GROUP-STUDIES:

Turbulence - Theory and Modelling GROUP-STUDIES: Lund Institute of Technology Department of Energy Sciences Division of Fluid Mechanics Robert Szasz, tel 046-0480 Johan Revstedt, tel 046-43 0 Turbulence - Theory and Modelling GROUP-STUDIES: Turbulence

More information

Numerical Investigation of the Fluid Flow around and Past a Circular Cylinder by Ansys Simulation

Numerical Investigation of the Fluid Flow around and Past a Circular Cylinder by Ansys Simulation , pp.49-58 http://dx.doi.org/10.1457/ijast.016.9.06 Numerical Investigation of the Fluid Flow around and Past a Circular Cylinder by Ansys Simulation Mojtaba Daneshi Department of Mechanical Engineering,

More information

AER1310: TURBULENCE MODELLING 1. Introduction to Turbulent Flows C. P. T. Groth c Oxford Dictionary: disturbance, commotion, varying irregularly

AER1310: TURBULENCE MODELLING 1. Introduction to Turbulent Flows C. P. T. Groth c Oxford Dictionary: disturbance, commotion, varying irregularly 1. Introduction to Turbulent Flows Coverage of this section: Definition of Turbulence Features of Turbulent Flows Numerical Modelling Challenges History of Turbulence Modelling 1 1.1 Definition of Turbulence

More information

Department of Energy Sciences, LTH

Department of Energy Sciences, LTH Department of Energy Sciences, LTH MMV11 Fluid Mechanics LABORATION 1 Flow Around Bodies OBJECTIVES (1) To understand how body shape and surface finish influence the flow-related forces () To understand

More information

Mechanical Measurements and Metrology Prof. S. P. Venkateshan Department of Mechanical Engineering Indian Institute of Technology, Madras

Mechanical Measurements and Metrology Prof. S. P. Venkateshan Department of Mechanical Engineering Indian Institute of Technology, Madras Mechanical Measurements and Metrology Prof. S. P. Venkateshan Department of Mechanical Engineering Indian Institute of Technology, Madras Module - 3 Lecture - 33 Measurement of Volume and Mass Flow Rate

More information

Numerical Simulation of the Evolution of Reynolds Number on Laminar Flow in a Rotating Pipe

Numerical Simulation of the Evolution of Reynolds Number on Laminar Flow in a Rotating Pipe American Journal of Fluid Dynamics 2014, 4(3): 79-90 DOI: 10.5923/j.ajfd.20140403.01 Numerical Simulation of the Evolution of Reynolds Number on Laminar Flow in a Rotating Pipe A. O. Ojo, K. M. Odunfa,

More information

Numerical and Experimental Study on the Effect of Guide Vane Insertion on the Flow Characteristics in a 90º Rectangular Elbow

Numerical and Experimental Study on the Effect of Guide Vane Insertion on the Flow Characteristics in a 90º Rectangular Elbow Numerical and Experimental Study on the Effect of Guide Vane Insertion on the Flow Characteristics in a 90º Rectangular Elbow Sutardi 1, Wawan A. W., Nadia, N. and Puspita, K. 1 Mechanical Engineering

More information

UNSTEADY DISTURBANCE GENERATION AND AMPLIFICATION IN THE BOUNDARY-LAYER FLOW BEHIND A MEDIUM-SIZED ROUGHNESS ELEMENT

UNSTEADY DISTURBANCE GENERATION AND AMPLIFICATION IN THE BOUNDARY-LAYER FLOW BEHIND A MEDIUM-SIZED ROUGHNESS ELEMENT UNSTEADY DISTURBANCE GENERATION AND AMPLIFICATION IN THE BOUNDARY-LAYER FLOW BEHIND A MEDIUM-SIZED ROUGHNESS ELEMENT Ulrich Rist and Anke Jäger Institut für Aerodynamik und Gasdynamik, Universität Stuttgart,

More information

Chapter 8 Performance analysis IV Accelerated level flight and climb (Lecture 27) Keywords: Topics 8.1 Introduction 8.2 Accelerated level flight

Chapter 8 Performance analysis IV Accelerated level flight and climb (Lecture 27) Keywords: Topics 8.1 Introduction 8.2 Accelerated level flight Chapter 8 Performance analysis I Accelerated level flight and climb (Lecture 7) Keywords: Accelerated level flight; accelerated climb; energy height. Topics 8.1 Introduction 8. Accelerated level flight

More information

Unsteady Volumetric Entropy Generation Rate in Laminar Boundary Layers

Unsteady Volumetric Entropy Generation Rate in Laminar Boundary Layers Entropy 6, 8[], 5-3 5 Entropy ISSN 99-43 www.mdpi.org/entropy/ Unsteady Volumetric Entropy Generation Rate in Laminar Boundary Layers E. J. Walsh & D. Hernon Stokes Research Institute, Dept. of Mechanical

More information

Bluff Body, Viscous Flow Characteristics ( Immersed Bodies)

Bluff Body, Viscous Flow Characteristics ( Immersed Bodies) Bluff Body, Viscous Flow Characteristics ( Immersed Bodies) In general, a body immersed in a flow will experience both externally applied forces and moments as a result of the flow about its external surfaces.

More information

Chapter 2 Lecture 7 Longitudinal stick fixed static stability and control 4 Topics

Chapter 2 Lecture 7 Longitudinal stick fixed static stability and control 4 Topics hapter 2 Lecture 7 Longitudinal stick ixed static stability and control 4 Topics 2.4.6 Revised expression or mcgt 2.4.7 mαt in stick-ixed case 2.5 ontributions o uselage to mcg and mα 2.5.1 ontribution

More information

UNIT 4 FORCES ON IMMERSED BODIES. Lecture-01

UNIT 4 FORCES ON IMMERSED BODIES. Lecture-01 1 UNIT 4 FORCES ON IMMERSED BODIES Lecture-01 Forces on immersed bodies When a body is immersed in a real fluid, which is flowing at a uniform velocity U, the fluid will exert a force on the body. The

More information

Experimental Investigation of the Aerodynamic Forces and Pressures on Dome Roofs: Reynolds Number Effects

Experimental Investigation of the Aerodynamic Forces and Pressures on Dome Roofs: Reynolds Number Effects Experimental Investigation of the Aerodynamic Forces and Pressures on Dome Roofs: Reynolds Number Effects *Ying Sun 1), Ning Su 2), Yue Wu 3) and Qiu Jin 4) 1), 2), 3), 4) Key Lab of Structures Dynamic

More information

Fundamentals of Aerodynamics

Fundamentals of Aerodynamics Fundamentals of Aerodynamics Fourth Edition John D. Anderson, Jr. Curator of Aerodynamics National Air and Space Museum Smithsonian Institution and Professor Emeritus University of Maryland Me Graw Hill

More information

FACULTY OF CHEMICAL & ENERGY ENGINEERING FLUID MECHANICS LABORATORY TITLE OF EXPERIMENT: MINOR LOSSES IN PIPE (E4)

FACULTY OF CHEMICAL & ENERGY ENGINEERING FLUID MECHANICS LABORATORY TITLE OF EXPERIMENT: MINOR LOSSES IN PIPE (E4) FACULTY OF CHEMICAL & ENERGY ENGINEERING FLUID MECHANICS LABORATORY TITLE OF EXPERIMENT: MINOR LOSSES IN PIPE (E4) 1 1.0 Objectives The objective of this experiment is to calculate loss coefficient (K

More information

APPLIED FLUID DYNAMICS HANDBOOK

APPLIED FLUID DYNAMICS HANDBOOK APPLIED FLUID DYNAMICS HANDBOOK ROBERT D. BLEVINS H imhnisdia ttodisdiule Darmstadt Fachbereich Mechanik 'rw.-nr.. [VNR1 VAN NOSTRAND REINHOLD COMPANY ' ' New York Contents Preface / v 1. Definitions /

More information

Project Topic. Simulation of turbulent flow laden with finite-size particles using LBM. Leila Jahanshaloo

Project Topic. Simulation of turbulent flow laden with finite-size particles using LBM. Leila Jahanshaloo Project Topic Simulation of turbulent flow laden with finite-size particles using LBM Leila Jahanshaloo Project Details Turbulent flow modeling Lattice Boltzmann Method All I know about my project Solid-liquid

More information

Module 3: Velocity Measurement Lecture 15: Processing velocity vectors. The Lecture Contains: Data Analysis from Velocity Vectors

Module 3: Velocity Measurement Lecture 15: Processing velocity vectors. The Lecture Contains: Data Analysis from Velocity Vectors The Lecture Contains: Data Analysis from Velocity Vectors Velocity Differentials Vorticity and Circulation RMS Velocity Drag Coefficient Streamlines Turbulent Kinetic Energy Budget file:///g /optical_measurement/lecture15/15_1.htm[5/7/2012

More information

Chapter 3 Lecture 7. Drag polar 2. Topics. Chapter-3

Chapter 3 Lecture 7. Drag polar 2. Topics. Chapter-3 hapter 3 eture 7 Drag polar Topis 3..3 Summary of lift oeffiient, drag oeffiient, pithing moment oeffiient, entre of pressure and aerodynami entre of an airfoil 3..4 Examples of pressure oeffiient distributions

More information

THE ROLE OF LOCALIZED ROUGHNESS ON THE LAMINAR-TURBULENT TRANSITION ON THE OBLIQUE WING

THE ROLE OF LOCALIZED ROUGHNESS ON THE LAMINAR-TURBULENT TRANSITION ON THE OBLIQUE WING THE ROLE OF LOCALIZED ROUGHNESS ON THE LAMINAR-TURBULENT TRANSITION ON THE OBLIQUE WING S.N. Tolkachev*, V.N. Gorev*, V.V. Kozlov* *Khristianovich Institute of Theoretical and Applied Mechanics SB RAS

More information

1. Introduction Some Basic Concepts

1. Introduction Some Basic Concepts 1. Introduction Some Basic Concepts 1.What is a fluid? A substance that will go on deforming in the presence of a deforming force, however small 2. What Properties Do Fluids Have? Density ( ) Pressure

More information